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    Lattice-free models of directed cell motility

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    Author
    Irons, C.
    Plank, M.J.
    Simpson, M.J.
    Date
    2016
    Permanent Link
    http://hdl.handle.net/10092/12341

    Directed cell migration often occurs when individual cells move in response to an external chemical stimulus. Cells can respond by moving in either the direction of increasing (chemoattraction) or decreasing (chemorepulsion) concentration. Many previous models of directed cell migration use a lattice-based framework where agents undergo a lattice-based random walk and the direction of nearest-neighbour motility events is biased in a preferred direction. Such lattice-based models can lead to unrealistic configurations of agents, since the agents always move on an artificial lattice structure which is never observed experimentally. We present a lattice-free model of directed cell migration that incorporates two key features. First, agents move on a continuous domain, with the possibility that there is some preferred direction of motion. Second, to be consistent with experimental observations, we enforce a crowding mechanism so that motility events that would lead to agent overlap are not permitted. We compare simulation data from the new lattice-free model with a more traditional lattice-based model. To provide additional insight into the lattice-free model, we construct an approximate conservation statement which corresponds to a nonlinear advection–diffusion equation in the continuum limit. The solution of this mean-field model compares well with averaged data from the individual-based model.

    Subjects
    advection
     
    chemotaxis
     
    biased random walk
     
    exclusion process
     
    nonlinear diffusion
     
    scratch assay
     
    Field of Research::01 - Mathematical Sciences
    Collections
    • Engineering: Journal Articles [1026]
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